Propagation Loss Prediction Considerations for Close-In Distances and Low-Antenna Height...

NTIA Report TR-07-449

Propagation Loss Prediction Considerations for Close-In Distances and Low-Antenna Height Applications

Nicholas DeMinco

NTIA Report TR-07-449

Propagation Loss Prediction

Considerations for Close-In Distances and Low-Antenna Height Applications

Nicholas DeMinco

U.S. DEPARTMENT OF COMMERCE

Carlos M. Gutierrez, Secretary

John M. R. Kneuer, Assistant Secretary for Communications and Information

July 2007

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DISCLAIMER

Certain commercial equipment and materials are identified in this report to specify adequately the technical aspects of the reported results. In no case does such identification imply recommendations or endorsement by the National Telecommunications and Information Administration, nor does it imply that the material or equipment identified is the best available for this purpose.

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CONTENTS

Page 1 INTRODUCTION................................................................................................................... 1 2 FUNDAMENTAL ANALYSIS CONSIDERATIONS FOR SHORT-RANGE AND LOW-ANTENNA PROPAGATION MODEL DEVELOPMENT ........................................ 5

2.1 Determination of the Far Field, Near Field, and Reactive Field for Typical Antennas...................................................................................................................... 6 2.2 The Flat-Earth Assumption, Distance to Horizon, Maximum Line-of-Sight Distance, and the First Fresnel Zone......................................................................... 14 2.3 The Significance of the Surface Wave for Loss Computations................................. 18 2.4 The Effects of the Earth on Antenna Patterns at Low Heights Above Earth............. 19 2.5 Mutual Coupling ........................................................................................................ 19

3 METHODS OF COMPUTING PROPAGATION LOSS FOR SHORT DISTANCES AND LOW-ANTENNA HEIGHTS............................................................... 21

3.1 Conventional Two-Ray Methods that Only Predict Propagation Loss Approximately........................................................................................................... 22 3.2 Sophisticated Propagation Loss Prediction Methods that Include All Effects .......... 23 3.3 Comparisons of the Undisturbed-Field Method with the Complex Two-Ray Method and Free-Space Propagation Loss................................................................ 26

4 CONCLUSIONS AND RECOMMENDATIONS ................................................................... 28 5 REFERENCES ........................................................................................................................ 30 APPENDIX A: SHORT-RANGE MOBILE-TO-MOBILE PROPAGATION MODEL STUDY SUMMARY.................................................................................................................... 31 A.1 INTRODUCTION......................................................................................................... 31 A.2 ENVIRONMENT DESCRIPTIONS............................................................................. 33

A.2.1 Urban High-Rise Environment .............................................................................. 33 A.2.2 Urban/Suburban Low-Rise Environment............................................................... 33 A.2.3 Residential Environment........................................................................................ 34 A.2.4 Rural Environment................................................................................................. 34 A.2.5 Indoor Environment ............................................................................................... 34

A.3 DISCUSSION OF AVAILABLE MODELS ................................................................ 34 A3.1 Survey of Models Available from the ITU-R Recommendations .......................... 35 A.3.2 Survey of Models Available in the Current Literature .......................................... 38

A.4 WHAT CAN BE USED FROM AVAILABLE MODELS AND WHAT NEEDS TO BE DEVELOPED?.................................................................................................. 56

A.4.1 Indoor Propagation................................................................................................. 56 A.4.2 Outdoor Propagation.............................................................................................. 57

A.5 CONCLUSION ............................................................................................................. 60 A.6 REFERENCES .............................................................................................................. 61

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APPENDIX B: PROPAGATION LOSS VS. DISTANCE WITH AND WITHOUT THE SURFACE WAVE........................................................................................................................ 65 APPENDIX C: ANTENNA ELEVATION PATTERNS FOR A VERTICAL HALF-WAVE DIPOLE AT DIFFERENT FREQUENCIES AND HEIGHTS ABOVE AVERAGE GROUND ................................................................................................................. 81 APPENDIX D: COMPARISON OF THE MUTUAL-COUPLING METHOD WITH THE UNDISTURBED-FIELD METHOD............................................................................................ 85 APPENDIX E: COMPARISON OF THE UNDISTURBED-FIELD METHOD WITH OTHER METHODS................................................................................................................... 101 APPENDIX F: COMPARISON OF THE UNDISTURBED-FIELD METHOD WITH OTHER METHODS (EXPANDED SCALES).......................................................................... 121

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FIGURES

Page Figure 1. Coordinate system geometry for field calculations......................................................... 8 Figure 2. Plotting the three original inequalities to determine far-field distance in wavelengths versus antenna aperture size normalized to wavelengths ........................................ 11 Figure 3. Plotting the three alternate inequalities to determine far-field distance in wavelengths versus antenna aperture size normalized to wavelengths. ....................................... 12 Figure 4. Far-field and near-field boundaries for a half-wave dipole and quarter-wave monopole....................................................................................................................................... 13 Figure 5. Distance at which the earth can be considered flat versus frequency ........................... 15 Figure 6. Comparison of simple two-ray model with complex two-ray model at 900 MHz........ 23 Figure B-1. Propagation loss vs. distance with and without the surface wave at 30 MHz for antenna heights h1=1m and h2=1m.......................................................................................... 66 Figure B-2. Propagation loss vs. distance with and without the surface wave at 30 MHz for antenna heights h1=2m and h2=1m.......................................................................................... 66 Figure B-3. Propagation loss vs. distance with and without the surface wave at 30 MHz for antenna heights h1=2m and h2=2m.......................................................................................... 67 Figure B-4. Propagation loss vs. distance with and without the surface wave at 30 MHz for antenna heights h1=3m and h2=1m.......................................................................................... 67 Figure B-5. Propagation loss vs. distance with and without the surface wave at 30 MHz for antenna heights h1=3m and h2=2m.......................................................................................... 68 Figure B-6. Propagation loss vs. distance with and without the surface wave at 30 MHz for antenna heights h1=3m and h2=3m. ....................................................................................... 68 Figure B-7. Propagation loss vs. distance with and without the surface wave at 150 MHz for antenna heights h1=1m and h2=1m.......................................................................................... 69 Figure B-8. Propagation loss vs. distance with and without the surface wave at 150 MHz for antenna heights h1=2m and h2=1m. ....................................................................................... 69 Figure B-9. Propagation loss vs. distance with and without the surface wave at 150 MHz for antenna heights h1=2m and h2=2m. ............................................................................................. 70

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Figure B-10. Propagation loss vs. distance with and without the surface wave at 150 MHz for antenna heights h1=3m and h2=1m. ....................................................................................... 70 Figure B-11. Propagation loss vs. distance with and without the surface wave at 150 MHz for antenna heights h1=3m and h2=2m.......................................................................................... 71 Figure B-12. Propagation loss vs. distance with and without the surface wave at 150 MHz for antenna heights h1=3m and h2=3m.......................................................................................... 71 Figure B-13. Propagation loss vs. distance with and without the surface wave at 300 MHz for antenna heights h1=1m and h2=1m.......................................................................................... 72 Figure B-14. Propagation loss vs. distance with and without the surface wave at 300 MHz for antenna heights h1=2m and h2=1m. ....................................................................................... 72 Figure B-15. Propagation loss vs. distance with and without the surface wave at 300 MHz for antenna heights h1=2m and h2=2m. ........................................................................................ 73 Figure B-16. Propagation loss vs. distance with and without the surface wave at 300 MHz for antenna heights h1=3 and h2=1............................................................................................... 73 Figure B-17. Propagation loss vs. distance with and without the surface wave at 300 MHz for antenna heights h1=3m and h2=2m. ........................................................................................ 74 Figure B-18. Propagation loss vs. distance with and without the surface wave at 300 MHz for antenna heights h1=3m and h2=2m. ....................................................................................... 74 Figure B-19. Propagation loss vs. distance with and without the surface wave at 450 MHz for antenna heights h1=1m and h2=1m.......................................................................................... 75 Figure B-20. Propagation loss vs. distance with and without the surface wave at 450 MHz for antenna heights h1=2m and h2=1m. ....................................................................................... 75 Figure B-21. Propagation loss vs. distance with and without the surface wave at 450 MHz for antenna heights h1=2m and h2=2m. ........................................................................................ 76 Figure B-22. Propagation loss vs. distance with and without the surface wave at 450 MHz for antenna heights h1=3m and h2=1m. ....................................................................................... 76 Figure B-23. Propagation loss vs. distance with and without the surface wave at 450 MHz for antenna heights h1=3m and h2=2m. ........................................................................................ 77 Figure B-24. Propagation loss vs. distance with and without the surface wave at 450 MHz for antenna heights h1=3m and h2=3m. ....................................................................................... 77

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Figure B-25. Propagation loss vs. distance with and without the surface wave at 900 MHz for antenna heights h1=1m and h2=2m. ........................................................................................ 78 Figure B-26. Propagation loss vs. distance with and without the surface wave at 900 MHz for antenna heights h1=2m and h2=1m.......................................................................................... 78 Figure B-27. Propagation loss vs. distance with and without the surface wave at 900 MHz for antenna heights h1=2m and h2=2m. ........................................................................................ 79 Figure B-28. Propagation loss vs. distance with and without the surface wave at 900 MHz for antenna heights h1=3m and h2=1m. ....................................................................................... 79 Figure B-29. Propagation loss vs. distance with and without the surface wave at 900 MHz for antenna heights h1=3m and h2=2m.......................................................................................... 80 Figure B-30. Propagation loss vs. distance with and without the surface wave at 900 MHz for antenna heights h1=3m and h2=3m. ....................................................................................... 80 Figure C-1. Elevation patterns for vertical half-wave dipole at 150 MHz. .................................. 82 Figure C-2. Elevation patterns for vertical half-wave dipole at 450 MHz. .................................. 82 Figure C-3. Elevation patterns for vertical half-wave dipole at 900 MHz. .................................. 83 Figure C-4. Elevation patterns for vertical half-wave dipole at 1750 MHz. ................................ 83 Figure C-5. Elevation patterns for vertical half-wave dipole at 3000 MHz. ................................ 84 Figure C-6. Elevation patterns for vertical half-wave dipole at 1590 MHz. ................................ 84 Figure D-1. Comparison of mutual coupling method with undisturbed field method at 150 MHz for antenna heights h1=1m and h2=1m. ........................................................................ 86 Figure D-2. Comparison of mutual coupling method with undisturbed field method at 150 MHz for antenna heights h1=2m and h2=1m. ....................................................................... 86 Figure D-3. Comparison of mutual coupling method with undisturbed field method at 150 MHz for antenna heights h1=3m and h2=1m. ........................................................................ 87 Figure D-4. Comparison of mutual coupling method with undisturbed field method at 150 MHz for antenna heights h1=2m and h2=2m. ........................................................................ 87 Figure D-5. Comparison of mutual coupling method with undisturbed field method at 150 MHz for antenna heights h1=3m and h2=2m. ........................................................................ 88

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Figure D-6. Comparison of mutual coupling method with undisturbed field method at 150 MHz for antenna heights h1=3m and h2=3m. ........................................................................ 88 Figure D-7. Comparison of mutual coupling method with undisturbed field method at 450 MHz for antenna heights h1=1m and h2=1m. ........................................................................ 89 Figure D-8. Comparison of mutual coupling method with undisturbed field method at 450 MHz for antenna heights h1=2m and h2=1m. ........................................................................ 89 Figure D-9. Comparison of mutual coupling method with undisturbed field method at 450 MHz for antenna heights h1=3m and h2=1m. ........................................................................ 90 Figure D-10. Comparison of mutual coupling method with undisturbed field method at 450 MHz for antenna heights h1=2m and h2=2m. ........................................................................ 90 Figure D-11. Comparison of mutual coupling method with undisturbed field method at 450 MHz for antenna heights h1=3m and h2=2m. ........................................................................ 91 Figure D-12. Comparison of mutual coupling method with undisturbed field method at 450 MHz for antenna heights h1=3m and h2=3m. ........................................................................ 91 Figure D-13. Comparison of mutual coupling method with undisturbed field method at 900 MHz for antenna heights h1=1m and h2=1m. ....................................................................... 92 Figure D-14. Comparison of mutual coupling method with undisturbed field method at 900 MHz for antenna heights h1=2m and h2=1m. ........................................................................ 92 Figure D-15. Comparison of mutual coupling method with undisturbed field method at 900 MHz for antenna heights h1=3m and h2=1m. ....................................................................... 93 Figure D-16. Comparison of mutual coupling method with undisturbed field method at 900 MHz for antenna heights h1=2m and h2=2m. ........................................................................ 93 Figure D-17. Comparison of mutual coupling method with undisturbed field method at 900 MHz for antenna heights h1=3m and h2=2m. ....................................................................... 94 Figure D-18. Comparison of mutual coupling method with undisturbed field method at 900 MHz for antenna heights h1=3m and h2=3m. ........................................................................ 94 Figure D-19. Comparison of mutual coupling method with undisturbed field method at 1750 MHz for antenna heights h1=1m and h2=1m. ..................................................................... 95 Figure D-20. Comparison of mutual coupling method with undisturbed field method at 1750 MHz for antenna heights h1=2m and h2=1m. ...................................................................... 95

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Figure D-21. Comparison of mutual coupling method with undisturbed field method at 1750 MHz for antenna heights h1=3m and h2=1m. ...................................................................... 96 Figure D-22. Comparison of mutual coupling method with undisturbed field method at 1750 MHz for antenna heights h1=2m and h2=2m. ...................................................................... 96 Figure D-23. Comparison of mutual coupling method with undisturbed field method at 1750 MHz for antenna heights h1=3m and h2=2m. ..................................................................... 97 Figure D-24. Comparison of mutual coupling method with undisturbed field method at 1750 MHz for antenna heights h1=3m and h2=3m. ...................................................................... 97 Figure D-25. Comparison of mutual coupling method with undisturbed field method at 3000 MHz for antenna heights h1=1m and h2=1m. ...................................................................... 98 Figure D-26. Comparison of mutual coupling method with undisturbed field method at 3000 MHz for antenna heights h1=2m and h2=1m. ...................................................................... 98 Figure D-27. Comparison of mutual coupling method with undisturbed field method at 3000 MHz for antenna heights h1=3m and h2=1m. ...................................................................... 99 Figure D-28. Comparison of mutual coupling method with undisturbed field method at 3000 MHz for antenna heights h1=2m and h2=2m. ...................................................................... 99 Figure D-29. Comparison of mutual coupling method with undisturbed field method at 3000 MHz for antenna heights h1=3m and h2=2 m. ................................................................... 100 Figure D-30. Comparison of mutual coupling method with undisturbed field method at 3000 MHz for antenna heights h1=3m and h2=3m. .................................................................... 100 Figure E-1. Comparison of the undisturbed field method with other methods at 150 MHz for antenna heights h1=1m and h2=1m........................................................................................ 102 Figure E-2. Comparison of the undisturbed field method with other methods at 150 MHz for antenna heights h1=2m and h2=1m........................................................................................ 102 Figure E-3. Comparison of the undisturbed field method with other methods at 150 MHz for antenna heights h1=3m and h2=1m. ........................................................................................... 103 Figure E-4. Comparison of the undisturbed field method with other methods at 150 MHz for antenna heights h1=2m and h2=2m........................................................................................ 103 Figure E-5. Comparison of the undisturbed field method with other methods at 150 MHz for antenna heights h1=3m and h2=2m. ...................................................................................... 104

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Figure E-6. Comparison of the undisturbed field method with other methods at 150 MHz for antenna heights h1=3m and h2=3m........................................................................................ 104 Figure E-7. Comparison of the undisturbed field method with other methods at 450 MHz for antenna heights h1=1m and h2=1m........................................................................................ 105 Figure E-8. Comparison of the undisturbed field method with other methods at 450 MHz for antenna heights h1=2m and h2=1m........................................................................................ 105 Figure E-9. Comparison of the undisturbed field method with other methods at 150 MHz for antenna heights h1=3m and h2=1m. ...................................................................................... 106 Figure E-10. Comparison of the undisturbed field method with other methods at 450 MHz for antenna heights h1=2m and h2=2m........................................................................................ 106 Figure E-11. Comparison of the undisturbed field method with other methods at 450 MHz for antenna heights h1=3m and h2=2m. ...................................................................................... 107 Figure E-12. Comparison of the undisturbed field method with other methods at 450 MHz for antenna heights h1=3m and h2=3m........................................................................................ 107 Figure E-13. Comparison of the undisturbed field method with other methods at 900 MHz for antenna heights h1=1m and h2=1m........................................................................................ 108 Figure E-14. Comparison of the undisturbed field method with other methods at 900 MHz for antenna heights h1=2m and h2=1m........................................................................................ 108 Figure E-15. Comparison of the undisturbed field method with other methods at 900 MHz for antenna heights h1=3m and h2=1m........................................................................................ 109 Figure E-16. Comparison of the undisturbed field method with other methods at 900 MHz for antenna heights h1=2m and h2=2m........................................................................................ 109 Figure E-17. Comparison of the undisturbed field method with other methods at 900 MHz for antenna heights h1=3m and h2=2m........................................................................................ 110 Figure E-18. Comparison of the undisturbed field method with other methods at 900 MHz for antenna heights h1=3m and h2=3m........................................................................................ 110 Figure E-19. Comparison of the undisturbed field method with other methods at 1590 MHz for antenna heights h1=1m and h2=1m........................................................................................ 111 Figure E-20. Comparison of the undisturbed field method with other methods at 1590 MHz for antenna heights h1=2m and h2=1m........................................................................................ 111

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Figure E-21. Comparison of the undisturbed field method with other methods at 1590 MHz for antenna heights h1=3m and h2=1m........................................................................................ 112 Figure E-22. Comparison of the undisturbed field method with other methods at 1590 MHz for antenna heights h1=2m and h2=2m........................................................................................ 112 Figure E-23. Comparison of the undisturbed field method with other methods at 1590 MHz for antenna heights h1=3m and h2=2m........................................................................................ 113 Figure E-24. Comparison of the undisturbed field method with other methods at 1590 MHz for antenna heights h1=3m and h2=3m........................................................................................ 113 Figure E-25. Comparison of the undisturbed field method with other methods at 1750 MHz for antenna heights h1=1m and h2=1m. ...................................................................................... 114 Figure E-26. Comparison of the undisturbed field method with other methods at 1750 MHz for antenna heights h1=2m and h2=1m........................................................................................ 114 Figure E-27. Comparison of the undisturbed field method with other methods at 1750 MHz for antenna heights h1=3m and h2=1m. ...................................................................................... 115 Figure E-28. Comparison of the undisturbed field method with other methods at 1750 MHz for antenna heights h1=2m and h2=2m........................................................................................ 115 Figure E-29. Comparison of the undisturbed field method with other methods at 1750 MHz for antenna heights h1=3m and h2=2m. ...................................................................................... 116 Figure E-30. Comparison of the undisturbed field method with other methods at 1750 MHz for antenna heights h1=3m and h2=3m........................................................................................ 116 Figure E-31. Comparison of the undisturbed field method with other methods at 3000 MHz for antenna heights h1=1m and h2=1m........................................................................................ 117 Figure E-32. Comparison of the undisturbed field method with other methods at 3000 MHz for antenna heights h1=2m and h2=1m. ............................................................................................ 117 Figure E-33. Comparison of the undisturbed field method with other methods at 3000 MHz for antenna heights h1=3m and h2=1m. ...................................................................................... 118 Figure E-34. Comparison of the undisturbed field method with other methods at 3000 MHz for antenna heights h1=2m and h2=2m........................................................................................ 118 Figure E-35. Comparison of the undisturbed field method with other methods at 3000 MHz for antenna heights h1=3m and h2=2m. ...................................................................................... 119

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Figure E-36. Comparison of the undisturbed field method with other methods at 3000 MHz for antenna heights h1=3m and h2=3m........................................................................................ 119 Figure F-1. Comparison of the undisturbed field method with other methods at 150 MHz for antenna heights h1=1m and h2=1m........................................................................................ 122 Figure F-2. Comparison of the undisturbed field method with other methods at 150 MHz for antenna heights h1=2m and h2=1m........................................................................................ 122 Figure F-3. Comparison of the undisturbed field method with other methods at 150 MHz for antenna heights h1=2m and h2=1m........................................................................................ 123 Figure F-4. Comparison of the undisturbed field method with other methods at 150 MHz for antenna heights h1=2m and h2=2m........................................................................................ 123 Figure F-5. Comparison of the undisturbed field method with other methods at 150 MHz for antenna heights h1=3m and h2=2m. ...................................................................................... 124 Figure F-6. Comparison of the undisturbed field method with other methods at 150 MHz for antenna heights h1=3m and h2=3m........................................................................................ 124 Figure F-7. Comparison of the undisturbed field method with other methods at 450 MHz for antenna heights h1=1m and h2=1m........................................................................................ 125 Figure F-8. Comparison of the undisturbed field method with other methods at 450 MHz for antenna heights h1=2m and h2=1m........................................................................................ 125 Figure F-9. Comparison of the undisturbed field method with other methods at 450 MHz for antenna heights h1=2m and h2=1m. ...................................................................................... 126 Figure F-10. Comparison of the undisturbed field method with other methods at 450 MHz for antenna heights h1=2m and h2=2m........................................................................................ 126 Figure F-11. Comparison of the undisturbed field method with other methods at 450 MHz for antenna heights h1=3m and h2=2m........................................................................................ 127 Figure F-12. Comparison of the undisturbed field method with other methods at 450 MHz for antenna heights h1=3m and h2=3m........................................................................................ 127 Figure F-13. Comparison of the undisturbed field method with other methods at 900 MHz for antenna heights h1=1m and h2=1m........................................................................................ 128 Figure F-14. Comparison of the undisturbed field method with other methods at 900 MHz for antenna heights h1=2m and h2=1m........................................................................................ 128

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Figure F-15. Comparison of the undisturbed field method with other methods at 900 MHz for antenna heights h1=3m and h2=1m........................................................................................ 129 Figure F-16. Comparison of the undisturbed field method with other methods at 900 MHz for antenna heights h1=2m and h2=2m........................................................................................ 129 Figure F-17. Comparison of the undisturbed field method with other methods at 900 MHz for antenna heights h1=3m and h2=2m........................................................................................ 130 Figure F-18. Comparison of the undisturbed field method with other methods at 900 MHz for antenna heights h1=3m and h2=3m........................................................................................ 130 Figure F-19. Comparison of the undisturbed field method with other methods at 1590 MHz for antenna heights h1=1m and h2=1m........................................................................................ 131 Figure F-20. Comparison of the undisturbed field method with other methods at 1590 MHz for antenna heights h1=2m and h2=1m........................................................................................ 131 Figure F-21. Comparison of the undisturbed field method with other methods at 1590 MHz for antenna heights h1=3m and h2=1m........................................................................................ 132 Figure F-22. Comparison of the undisturbed field method with other methods at 1590 MHz for antenna heights h1=2m and h2=2m........................................................................................ 132 Figure F-23. Comparison of the undisturbed field method with other methods at 1590 MHz for antenna heights h1=3m and h2=2m. ...................................................................................... 133 Figure F-24. Comparison of the undisturbed field method with other methods at 1590 MHz for antenna heights h1=3m and h2=3m........................................................................................ 133 Figure F-25. Comparison of the undisturbed field method with other methods at 1750 MHz for antenna heights h1=1m and h2=1m. ............................................................................................ 134 Figure F-26. Comparison of the undisturbed field method with other methods at 1750 MHz for antenna heights h1=2m and h2=1m........................................................................................ 134 Figure F-27. Comparison of the undisturbed field method with other methods at 1750 MHz for antenna heights h1=3m and h2=1m. ...................................................................................... 135 Figure F-28. Comparison of the undisturbed field method with other methods at 1750 MHz for antenna heights h1=2m and h2=2m........................................................................................ 135 Figure F-29. Comparison of the undisturbed field method with other methods at 1750 MHz for antenna heights h1=3m and h2=2m........................................................................................ 136

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Figure F-30. Comparison of the undisturbed field method with other methods at 1750 MHz for antenna heights h1=3m and h2=3m........................................................................................ 136 Figure F-31. Comparison of the undisturbed field method with other methods at 3000 MHz for antenna heights h1=1m and h2=1m........................................................................................ 137 Figure F-32. Comparison of the undisturbed field method with other methods at 3000 MHz for antenna heights h1=2m and h2=1m........................................................................................ 137 Figure F-33. Comparison of the undisturbed field method with other methods at 3000 MHz for antenna heights h1=3m and h2=1m........................................................................................ 138 Figure F-34. Comparison of the undisturbed field method with other methods at 3000 MHz for antenna heights h1=2m and h2=2m........................................................................................ 138 Figure F-35. Comparison of the undisturbed field method with other methods at 3000 MHz for antenna heights h1=3m and h2=2m........................................................................................ 139 Figure F-36. Comparison of the undisturbed field method with other methods at 3000 MHz for antenna heights h1=3m and h2=3. ......................................................................................... 139

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TABLES

Page Table 1. Maximum Line-of-Sight Distance Between Two Antennas on a Spherical Earth Versus Antenna Heights for Two Values of Effective Earths Radius..................................................... 16 Table 2. Distance df in Meters of the First Fresnel Zone Clearance as a Function of Antenna Heights and Frequency/Wavelength. ............................................................................................ 17

PROPAGATION LOSS PREDICTION CONSIDERATIONS FOR CLOSE-IN DISTANCES AND LOW-ANTENNA HEIGHT APPLICATIONS

Nicholas DeMinco1

An investigation of different propagation modeling methods to meet the special requirements of a short-range propagation model with low antenna heights was performed, and has resulted in the development of approaches to be taken to accurately model radio-wave propagation loss for these types of scenarios. The basic requirements for the Short-Range Mobile-to-Mobile Propagation Model include: separation distances between the transmitter and receiver from one meter to two kilometers, a frequency range of 150 MHz to 3000 MHz, and antenna heights of one to three meters for both transmitter and receiver sites. It is necessary to develop alternative methods for accurate predictions of propagation loss to provide a propagation model that will simultaneously meet all of these requirements. This will require special considerations that currently available models do not include in their methods of analysis. Several analytical approaches were investigated to develop propagation loss prediction methods that take all of these considerations into account. Analysis efforts have determined that the development of this model will require the use of mutual-coupling predictions and should also include the effects of the surface wave. Conventional far-field antenna patterns and gain of the antennas may also not be valid at close separation distances, since one antenna may not be in the far field of the other antenna. Analysis efforts have also determined that these issues and effects become more significant for the lower frequencies (900 MHz and below). For low antenna heights the effects of the close proximity between the Earth and the antenna produce a strong interaction between the antenna and the ground. The antenna pattern performance is vastly different than if the antenna were in free space.

Key words: antennas; low antenna heights; mobile communications; mutual coupling; propagation modeling; radio-wave propagation

1 INTRODUCTION

1 The author is with the Institute for Telecommunication Sciences, National Telecommunications and Information Administration, U.S. Department of Commerce, Boulder, CO 80305.

With the tremendous growth in demand for licensed and unlicensed mobile wireless devices, it is necessary for regulatory agencies to perform electromagnetic compatibility analyses to address the problems of interference between users of the electromagnetic spectrum to accommodate the increasing number and type of these new mobile devices. The evolution of our communications

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infrastructure depends heavily on the use of these licensed and unlicensed mobile communication devices. The growth and prosperity of our economy depends on the successful operation and compatible coexistence of these wireless devices in a crowded electromagnetic spectrum. An accurate and flexible radio-wave propagation model is essential for meeting the needs of both the spectrum management process and the electromagnetic compatibility analysis process. In an Executive Memorandum from the President dated November 30, 2004, the Department of Commerce was requested to submit a plan to implement recommendations that would ensure that our spectrum management policies are capable of harnessing the potential of rapidly changing technologies. These recommendations included providing a modernized and improved spectrum management system for more efficient and beneficial use of the spectrum. In addition, these recommendations included developing engineering analysis tools to facilitate the deployment of new and expanded services and technologies, while preserving national security and public safety, and encouraging scientific research and development of new technologies. In meeting these recommendations in the area of engineering analyses and technology assessments, it will be necessary to determine the best practices in engineering related to spectrum management, and also address the electromagnetic compatibility analysis process. In response to this Executive Memorandum, the National Telecommunications and Information Administration/Office of Spectrum Management (NTIA/OSM) tasked the Institute for Telecommunication Sciences (ITS) to determine what radio-wave propagation models currently existed and whether or not they could be used reliably for electromagnetic compatibility analyses and for spectrum management of mobile wireless devices that were very close to each other (distances of one meter to two kilometers) and located at very low antenna heights (one to three meters). ITS reviewed all currently available propagation models in the literature and also those described in the International Telecommunication Union Radiocommunication Sector (ITU-R) Recommendations to determine their applicability. Even though the models that were examined have their own regions of validity with respect to frequency, separation distance, and antenna heights, they were all found to be inadequate for simultaneously meeting the short-range mobile-to-mobile model requirements of: one meter to two kilometer separation distances, one to three meter antenna heights, and a frequency range of 150 MHz to 3000 MHz. Existing radio-wave propagation models are valid only for much higher antenna heights (four meters or greater) and larger separation distances (greater than ten meters). Providing a propagation model that will simultaneously account for close-in distances on the order of one meter, low antenna heights of one to three meters, and frequencies as low as 150 MHz will require special considerations that currently available models do not include in their methods of analysis. It was therefore necessary to initiate an analysis effort to develop alternative models that would be valid in this parameter range. A preliminary analysis effort was initiated for developing alternative radio-wave propagation models that would perform predictions that would be valid for these frequencies, separation distances and low antenna heights typical of the new generation of short-range Mobile-to-Mobile (MTOM) communication devices. The analysis has determined that this requires the use of mutual-coupling predictions and should also include the effects of the surface wave, and the near-field effects of the antennas for these frequencies. The antenna

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patterns or gains of the antennas may not be valid at close separation distances, since they may not be in the far-field region of the antennas. Conventional far-field antenna patterns of the antennas may also not be valid at close separation distances, since one antenna may not be in the far field of the other. These issues and effects become more significant for the lower frequencies (900 MHz and below). In addition, the analysis determined that for low antenna heights, the effects of the close proximity of the Earth to the antenna produce a strong interaction of the antenna with ground, changing its impedance and thus affecting the efficiency and gain of the antennas. The antenna impedance is affected when the antenna is within a half-wavelength above the Earth ground. Existing radio-wave propagation models separate the antennas from the propagation loss, and calculate a basic transmission loss that is independent of the antennas. At short separation distances and low antenna heights, it is necessary to develop radio-wave propagation models that include the interaction of the antennas and the radio-wave propagation loss. The effects of the presence of the Earth on the antennas and the propagation loss must also be included. Investigations of different propagation modeling methods and the special considerations of a short-range propagation model with low antenna heights have resulted in the development of alternative approaches to be taken to accurately model propagation loss in a mobile-to-mobile environment. A hierarchy of approaches were investigated that could be used to develop the short-range MTOM model. These approaches would account for different levels of complexity from very simplistic models where not much information about the scenario was known, to increasingly more sophisticated models that include all of the previously mentioned effects for scenarios where more site-specific information would be available. For example, free-space loss is the least complex and least accurate method, and a mutual-coupling method including all effects is the most complex and most accurate method. A method of intermediate complexity is the complex two-ray theory with complex reflection coefficient and antenna effects included. These methods and others will be discussed in this report. In future efforts, mathematical algorithms for radio-wave propagation models will be developed from the results of this analysis. This report describes the considerations that are involved in developing a model to meet these requirements for the line-of-sight (LOS) scenarios. This initial analysis addressed the LOS propagation environment in an open scenario for vertical polarization. Horizontal polarization will be addressed in future efforts. A future study will cover non-LOS scenarios. Future analysis and measurement efforts to be performed will address LOS and non-LOS scenarios for: the urban/suburban canyon environment, the suburban/residential environment, the parking lot canyon, and the rural environment. The preliminary analysis effort has determined what technical considerations need to be included in a radio-wave propagation loss prediction model for short-distances and low-antenna heights. Investigations were made of various propagation computation methods and mutual-coupling calculations. This information will be used in future efforts to develop radio-wave propagation models for the short-range MTOM model. Section 2 describes the fundamental analysis considerations that need to be addressed for short-

4

range, low-antenna propagation prediction model development. Section 3 describes propagation loss prediction methods that were investigated for use in a short-range, low antenna propagation environment. Section 4 describes the results of this investigation and recommends the approaches to use in the development of a short-range, low-antenna propagation prediction model. Appendix A is a reworked version of a contractor report written by this author, titled Short-Range Mobile-to-Mobile Propagation Model Study Summary, completed in September 2006. It describes the results of an investigation of what radio-wave propagation loss prediction models currently exist in the literature and ITU-R Recommendations, and discusses why they are inappropriate for simultaneously meeting all of the requirements of the short-range MTOM model. Appendices B through F contain large numbers of figures that are referred to in various sections of the main body of the report. Due to the large number of figures in each appendix, it would be inappropriate to integrate these into their corresponding sections. Appendix B is referred to in Section 2.3 and contains predicted propagation loss versus distance plots that demonstrate the significance of including the surface wave in propagation loss computations at six combinations of antenna heights and five different frequencies. Appendix C is referred to in Section 2.4 and contains computed antenna elevation patterns for a vertical half-wave dipole at six different frequencies for antenna heights of 1, 2, and 3 meters above average ground demonstrating the effects of the presence of ground. Also shown is the free-space elevation antenna pattern. Appendix D is referred to in Section 3.2 and contains plots of predicted propagation loss versus distance for six combinations of antenna heights and five frequencies that compare the results for the mutual-coupling method with the results of the undisturbed-field method. These plots show that the undisturbed field method achieves very similar results to that of the mutual-coupling method. Appendices E and F are referred to in Section 3.3 and contain plots of predicted propagation loss versus distance for six different frequencies and six combinations of antenna heights that compare four different propagation loss prediction methods: the free-space loss method, two versions of the complex two-ray method, and the undisturbed-field method. Appendix E plots contain the predicted loss out to 30 meters and Appendix F plots contain the predicted loss out to 10 meters with an expanded scale to provide more detail of the short range behavior of the different propagation prediction methods.

5

2 FUNDAMENTAL ANALYSIS CONSIDERATIONS FOR SHORT-RANGE AND LOW-ANTENNA PROPAGATION MODEL DEVELOPMENT

This section describes the analysis considerations used to determine those factors that are important for obtaining an accurate prediction of radio-wave propagation loss in a short-distance environment with low antenna heights that would be valid at frequencies over the 150- to 3000- MHz frequency range. The considerations for the development of the Short-Range MTOM Propagation Model to meet the above requirements at frequencies as low as 150 MHz and make accurate propagation loss predictions will be discussed. Satisfying all three of the above requirements simultaneously for frequencies as low as 150 MHz, increases the complexity needed for the model or group of models to meet the objectives of providing accurate propagation loss predictions. Initially, a literature search was performed where only a small percentage of the references were found to be even partially applicable for the short-range MTOM model, since none of the models and measured data in the currently existing literature references or ITU-R Recommendations can provide an accurate analysis and meet all of these requirements simultaneously. Section A.4 of Appendix A describes the areas where these references and Recommendations can be used for analyses on a limited basis. They can provide propagation loss predictions for only part of the needed frequency band, only the longer distances of the required distance range, and only the higher antenna heights. In addition, they can only be applicable for certain scenarios of the desired environment. Even a combination of these models could not meet all of these requirements of the short-range MTOM model for any significant amount of the frequency band, distances, or antenna heights. A discussion in Section 2.1 of the determination of reactive near-field region, radiating near-field region, and radiating far-field region distances of an antenna will show how they are based not only on aperture size and frequency, but also on phase error, amplitude error, and the reduction of the higher order terms of near-field reactive region and near-field radiated-field region terms. Computations of far-field region, near-field region and reactive-field region distances for all frequencies based on aperture size will determine what distances are applicable for small antennas. A discussion of how far out in distance the Earth is flat as a function of frequency in Section 2.2 will show that for distances less than about 5 kilometers, the Earth can be considered flat for radio-wave propagation purposes. The distance to horizon, maximum LOS distance between two antennas, and the first Fresnel zone between two antennas will also be computed as a function of antenna heights in Section 2.2. Six antenna height combinations will be presented for maximum LOS distance between two antennas and the distance to the first Fresnel zone. A discussion of how this first Fresnel zone computation is related to the two-ray breakpoint model, and how it is used to generate a LOS propagation model is described in Section A.3.2 of Appendix A.

6

The propagation loss computations with and without the surface wave discussed in Section 2.3 will show the significance of the surface wave for six combinations of antenna heights from 150 to 900 MHz over close-in distances. A description of elevation coverage plots for a dipole antenna as a function of frequency and antenna heights will be presented in Section 2.4 to demonstrate the effects of the Earth on antenna radiation pattern performance. Section 2.5 is a discussion of mutual coupling and how it affects a computation of propagation loss.

2.1 Determination of the Far Field, Near Field, and Reactive Field for Typical Antennas There are three field regions surrounding an antenna: the radiating far-field region also known as the Fraunhofer region, the radiating near-field region also known as the Fresnel region, and the non-radiating reactive near-field region closest to the antenna. The following discussion will describe how to determine these near- and far-field regions for different types of antennas. In the far-field region of an antenna, the electromagnetic fields exhibit plane wave behavior. The radiating far-field region of an antenna is also characterized as having an angular field distribution that is independent of the radial distance from the antenna. When the transmitter and the receiver are at a separation distance such that the far-field region conditions are satisfied for both of the antennas, then antenna parameters such as gain and radiation patterns can be used to make performance and interference analyses. The radiation pattern of an antenna in the far-field region is independent of distance, r, and hence the angular field distribution of the fields from the antenna will not depend on distance. The electromagnetic fields have a 1/r dependence, and only the transverse components of the electric and magnetic field are present. The ratio of the electric to magnetic field in free space is 377 ohms in the far-field region. Over real ground this ratio can be different from 377 ohms in the far-field region. This ratio can also be different in the near- field region of the antennas. For these reasons it is informative to know where the reactive near- field region, the radiating near-field region, and the far-field region of the antenna occur for different size apertures. The radiating near-field region of an antenna occurs in a radial distance range that lies between the reactive near-field region and the radiating far-field region of the antenna. Fields exhibit non-plane wave behavior in this region, and their angular field distribution is dependent on the radial distance from the antenna. Even closer to the antenna, the amplitude of the electromagnetic fields in the reactive near-field region dominates over the amplitude of the electromagnetic fields in the radiating near-field region. For an antenna whose maximum dimension is small compared to a wavelength at the operating frequency, the radiating near-field region may not exist. For most antennas with a maximum aperture dimension of D and where D>>, the radiating near-field region begins at an approximate distance of r = 0.62 (D3/)0.5 , and extends out to the beginning of the far-field region of the antenna [1]. The reactive near-field region starts at the antenna surface and extends out to this distance r. The D>>

condition is not fulfilled for the half-wave dipole and the quarter-wave monopole antennas, so this approximation cannot be used to determine the boundary where the reactive near field begins and the radiated near field ends for such antennas. For a small dipole or monopole antenna, the distance defining where the reactive near-field region ends and the radiating near-field region begins will be r = /2 or (0.159). This distance of r = /2 is also where the maximum powers in the near-field radiating and near-field reactive regions are equal [1]. The beginning of the far-field region, where the fields exhibit plane-wave behavior, depends on the aperture size with respect to a wavelength. There are three conditions that must be satisfied for distance r to be in the far-field region of an antenna [1]. These conditions are stated as inequalities below.

>>r D >>r D 2 >r

2

(1)

where D is the maximum dimension of the aperture. All three of these conditions must be satisfied simultaneously for an observation point to be in the far-field region of an antenna. These conditions are based on certain criteria for phase and amplitude errors in addition to reduction of 1/r2 and 1/r3 terms in the near-field region electric and magnetic fields. The first inequality, r > 2D2/ is based on achieving a maximum phase difference, from one end of the aperture to the center of the aperture, that is less than a specified amount (the parallel ray approximation), so that the antenna can be considered to be in the far-field region. This depends on the specific antenna type and antenna size in wavelengths, but for most antennas whose maximum dimension is large compared to a wavelength, the maximum phase difference of /16 is used [2]. The maximum phase difference of /16 corresponds to r=2D2/. Some antennas require a smaller phase difference to get better null performance and sidelobe detail, and therefore the separation distance must be larger [2]. Most of the antennas for mobile-to-mobile communications can be modeled as a monopole or dipole antenna or combination of these antennas. The analysis that follows can be expanded to apply to other antennas. A monopole or dipole antenna can be modeled using a line source in the form of a short current element. Consider a short current element of length z' along the z-axis. The symmetry of this current element about the z-axis allows the simplification of confining the field observation points to the yz plane. The distance R in Figure 1 is then given by: )'z -z ( + y = R 22 (2)

7

The field coordinates can be put in terms of a spherical coordinate system using the coordinate transformations.

(3) r =y r =z z +y = r 222

sincos

Figure 1. Coordinate system geometry for field calculations. Using these coordinate transformations the distance R in spherical coordinates is then: )'cos' (z + z r 2 - r = R 22 (4)

Expanding this equation using the binomial expansion theorem, the equation for distance R from any point along the length of an antenna aperture to the observation point in terms of the distance r from the center of the antenna aperture is given as [2]:

+ r2

(z + 2r

(z + z -r = R2

2322 cossin)'sin)'cos' (5)

8

Where z' is the distance along the antenna aperture from the origin, and is the angle measured from the z axis (Figure 1). If only the first two terms are used to represent the distance to the far- field region observation point, then the error is represented by the third and fourth terms. The third term is the most significant and attains its maximum value at = /2. The fourth term vanishes at = /2 in addition to the fifth and higher order terms [2]. The reactive near-field

region extends out to distance r, where the fourth term of the equation for radiated field achieves its maximum value of /8 [2]. Therefore, the third term represents the maximum total phase error of neglecting the third term in the far-field region approximation. A maximum total phase error of /8 radians (/16) is usually acceptable for most antennas with maximum aperture dimensions greater than a wavelength [2]. This /8 phase error is also acceptable for small antennas such as very short dipoles and monopoles. For z'D/2, and setting 2/ times the third term of the above equation equal to /8, then r 2D2/. If the maximum tolerable phase error had been specified as /16 (/32), then r 4D2/. The second inequality, r>>D, determines the amplitude error associated with assuming the magnitude of R is similar to that of r, where R is the distance from any point along the length of the dipole antenna aperture to the point of observation, and r is the distance from the center of the aperture to the point of observation (Figure 1). The distance R can be described in rectangular coordinates in terms of r from the geometry of Figure 1 as [2]:

/2 = for (z + r = R

(z + z r 2 - r = R22

22

)'

)'cos' (6)

The maximum amplitude error between R and r occurs at = /2. If z' = D/2, and r = 5D, then R= 5.0249D. The relative amplitude ratio, r/R is then equal to 0.991, and the relative amplitude error is (R-r)/r = 0.005 or one-half percent. The third inequality r >> is a requirement to reduce the magnitude of the higher order terms (1/r2 and 1/r3) of the electric and magnetic fields of the radiation field of the antenna, so that only the 1/r far-field terms are significant. The 1/r2 and 1/r3 terms are near-field radiating and reactive field terms, respectively, that decay rapidly with increasing distance from the antenna. This requirement originates from the equations for the electric or magnetic fields of the antenna and satisfies the inequality r >> 1, where = 2/ [2]. The equation for the total electric and magnetic fields of a short vertical dipole antenna is [2]:

=

r

e rj

1 + 1 j 4

z I = H

r

e rj -

r1

2z I = E

r

e )r(

1 - rj

1 + 1 j 4

z I = E

rj-

rj-

2r

r-j

2

sin

cos

sin

(7)

9

where = 2f, is the permeability of the medium, is the dielectric constant of the medium, and is the intrinsic impedance of the medium = 377 ohms in free space. If r = 10, then the 1/r2 term is ten percent of the 1/r term, and the 1/r3 term is one percent of the 1/r term. The distance requirement to be in the far-field region is then r>1.6.

1.6 > r

10 > r 2 = r (8)

If r = 20, then the 1/r2 term is five percent of the 1/r term, and the 1/r3 term is one-half percent of the 1/r term. The distance requirement to be in the far-field region is then r > 3.2. A method of plotting these three inequalities r > 2D2 /, r >> D with r > 5D, and r>> with r > 1.6 has been described in [1,3] to determine the distance to the far-field region of any antenna that will satisfy all three equations simultaneously. The results show the distance to the far-field region of an antenna normalized to wavelengths, r/ plotted in terms of aperture electrical size, D/. One author [3] plotted these equations as suggested in [1], and showed the regions of validity in terms of antenna aperture size, D/. Figure 2 shows a plot for the following inequalities plotted as three curves from the equations for all values of the range of D/ where the greater than sign has been replaced by an equals sign. The normalized distance to the far-field region is dominated by the first curve (black) up to a normalized aperture of 0.32. The second curve (red) shows that the normalized distance to the far-field region dominates for normalized apertures between 0.32 and 2.5. The third curve (blue) shows that the normalized distance to the far-field region dominates for all larger normalized apertures greater than 2.5. Amplitude considerations dominate for small apertures, while phase considerations dominate for large apertures.

22Dr > for D > 2.50

r > 5D for 0.32 D 2.50 r > 1.6 for D < 0.32

(9)

10

0

5

10

15

20

0 1 2 3

r/ = 1.6r/ = 5D/r/ = 2D2 /2

Aperture Size Normalized to Wavelength (D/)

Dis

tanc

e N

orm

aliz

ed to

Wav

elen

gth

(r/)

Figure 2. Plotting the three original inequalities to determine far-field distance in wavelengths versus antenna aperture size normalized to wavelengths.

The criteria for the three conditions can be adjusted to suit the application and achieve the desired reduction in relative magnitudes of the higher-order field components and the desired phase and amplitude errors. The regions of validity based on aperture size could change with how one selects the right-hand side of these three inequalities, but if the right-hand sides of these inequalities are each multiplied by the same numerical factor to obtain greater or lesser accuracy, then the regions along the boundaries for the horizontal axis of validity based on aperture size will stay the same. The regions of validity are determined by the intersections of the three equations in this plot, and the areas or regions on the graph that satisfy all three inequalities simultaneously. The distance r must be greater than that specified by all three of the inequalities.

11

If the right-hand sides of each of these inequalities are each multiplied by a different factor, then the boundaries will change for the regions of validity in terms of aperture size. An example will illustrate this. When the inequalities are multiplied by the different factors, for example: r>2D2/, r>3D, and r>2, these inequalities can be plotted as far-field distance normalized to wavelength along the y-axis, r/, versus aperture size normalized to wavelength along the x-axis,

D/, to determine the far-field regions of validity as a function of antenna aperture size as shown in Figure 3. All three inequalities must be satisfied simultaneously for an observation point to be in the far-field region of an antenna, whose maximum aperture size is D. The regions of validity for each inequality are then obtained from the resulting plots of Figure 3 as:

22Dr > for D > 1.50

r > 3D for 0.67 D 1.50 r > 2.0 for D < 0.67

(10)

0

5

10

15

20

0 1 2 3

r/ = 2.0r/ = 3D/r/ = 2D2/2

Aperture Size Normalized to Wavelength (D/)

Dis

tanc

e N

orm

aliz

ed to

Wav

elen

gth

(r/)

Figure 3. Plotting the three alternate inequalities to determine far-field distance in wavelengths versus antenna aperture size normalized to wavelengths. The maximum tolerable error for the first expression r>2D2/ is /8 or /16 as before. The maximum relative amplitude error for the second expression r>3D with r=3D and z=D/2, is

12

(R-r)/r = 0.0136 or about 1.36 percent. For this case R= 3.041D and the relative amplitude r/R = 0.986. The third expression r>2.0 corresponds to r = 2, and the 1/r2 term is approximately 7.9 percent of the first term. The 1/r3 term is approximately 0.63 percent of the first term. The

inequalities can also be solved algebraically to determine the intersection points that divide the regions of validity, and then evaluate the inequalities on either side of the intersection points to determine which inequalities set the distance to the far-field region. Plotting the inequalities as described above is the easier method and more illustrative in determining the regions of validity than solving the equations algebraically. The original criteria described in the original equations above with r>2D2/, r>5D, and r>1.6, will be used for this analysis. This is shown in Figure 2. For all quarter-wave antennas, since D1.6 is the determining inequality in all cases, since it is greater than the other two inequalities, and one graph can be plotted showing the far-field distance versus frequency (Figure 4). The far field for half-wave dipole antennas is determined by the expression r>5D, since 0.32

2.2 The Flat-Earth Assumption, Distance to Horizon, Maximum Line-of-Sight Distance, and the First Fresnel Zone

The Earth can be considered flat out to a distance d in kilometers given by [4]:

] (MHz) f [

80 = d(km) 1/3 (11)

14

Figure 5 is a plot of this distance versus frequency. It can be seen that the Earth is flat out to over 5 kilometers over the entire frequency range from 150 MHz to 3000 MHz. The flat-Earth assumption for the short-range MTOM propagation model is valid over the entire frequency range, since our maximum distance requirement is 2 kilometers.

5

6

7

8

9

10

11

12

13

14

15

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000

Frequency (MHz)

Dis

tanc

e (k

ilom

eter

s)

Figure 5. Distance at which the earth can be considered flat versus frequency. The distance to the horizon over a spherical Earth without terrain is a function of the heights of the transmitter and receiver antennas and the effective Earths radius, ae= ka, where a is the Earths radius in meters and k is the effective Earths radius factor. The distance d in kilometers to the horizon for an antenna height h in meters is given by [5]: 2kah = d (12)

It follows that the maximum line-of-sight distance in kilometers between two antennas at heights h1 and h2 in meters is: 21 22 kah + kah = d (13)

15

The maximum line-of-sight distance in kilometers between two antennas at heights h1 and h2 in meters for k= 4/3 is given by: ( )(m) h + (m) h 4.1215 = (km) d 21 (14)

The shortest line-of-sight distance between two antennas occurs when k=2/3. The shortest maximum line-of-sight distance in kilometers between two antennas at heights h1 and h2 in meters for k= 2/3 is given by: ( ) (m) h + (m) h 2.9143 = (km) d 21 (15)

Table 1 lists the maximum line-of-sight distances between two antennas for both values of k for the antenna heights of both antennas in the range of 1 to 3 meters. The smallest of these distances is about 6 kilometers, so the line-of-sight condition exists for all antenna heights in this range and within the 2-kilometer range requirements for the model, and the Earth can still be considered flat. This table holds for spherical Earth without terrain. Terrain and building obstructions on the path will reduce the distances and must be treated on a case by case basis using terrain information and other mathematical equations. Table 1. Maximum Line-of-Sight Distance Between Two Antennas on a Spherical Earth Versus Antenna Heights for Two Values of Effective Earths Radius h1 (meters)

h2 (meters)

d(km) for k= 4/3

d(km) for k=2/3

1

1

8.24

5.83

2

1

9.95

7.06

3

1

11.26

7.96

2

2

11.66

8.24

3

2

12.97

9.17

3

3

14.28

10.10

The first Fresnel zone over flat Earth in the region of two antennas can be defined as an ellipsoid with the transmit antenna located at one of the foci, and the receive antenna located at the other foci. The first Fresnel zone is where the path length from one antenna to a point on the ellipsoid and then on to the other antenna is /2 longer than the direct path between the antennas. For propagation analysis, a breakpoint can be defined as the distance at which the ground or other object begins to obstruct the first Fresnel zone. At distances less than that distance which has first Fresnel zone clearance, the propagation loss is due to the spherical spreading loss of the

16

wavefront (free-space propagation) and the vector addition and subtraction of the direct and reflected wave. At distances greater than that distance which has first Fresnel zone clearance, the propagation loss becomes greater. The distance in meters df at which the first Fresnel zone becomes obstructed as a function of antenna heights h1 and h2, and wavelength in meters, is given by [6]: /2)( + /2)( )h + h( 4 - h h 16 1/ = (m) d 422

21

22

21

2f (16)

Table 2 lists the distance df as a function of the antenna heights and wavelength. Table 2. Distance df in Meters of the First Fresnel Zone Clearance as a Function of Antenna Heights and Frequency/Wavelength h1 (m)

h2 (m)

df (m) f=150 MHz = 2m

df (m) f=300 MHz = 1m

df (m) f=450 MHz = .667m

df (m) f=900 MHz = .333m

df (m) f=1500 MHz = .200m

df (m) f=1800 MHz = .167m

df (m) f=3000 MHz = .100m

1

1

1.5

3.75

5.83

11.93

19.95

23.95

39.98

2

1

3.35

7.69

11.78

23.92

39.94

47.94

79.97

3

1

5.12

11.58

17.71

35.90

59.92

71.92

119.96

2

2

7.50

15.75

23.82

47.96

79.95

95.94

159.98

3

2

11.46

23.73

35.80

71.98

119.95

143.93

239.97

3

3

17.50

35.75

53.81

108.02

179.95

215.92

359.98

The distance at which the first Fresnel zone becomes obstructed represents a breakpoint for the curve that describes LOS propagation loss. It is related and similar to the breakpoint for the two-ray theory. The two-slope/breakpoint method can be matched with the two-ray LOS model, and the distance to the first Fresnel zone is the location of the breakpoint. The shape of the envelope of the two-ray theory matches that of the two-slope/breakpoint model. The distance of the breakpoint from the transmitter is equal to the maximum distance that has first Fresnel zone clearance. At distances less than the breakpoint for the two-ray theory, the signal strength or propagation loss oscillates due to the constructive and destructive interference between the direct and reflected waves. At distances greater than the breakpoint, the signal decreases or the loss increases at a much faster rate than before the breakpoint. This information can be used to construct a double regression model that can represent the propagation loss for a line-of-sight scenario. A discussion of how this double regression model can be used to fit measured data can be found in Appendix A.

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2.3 The Significance of the Surface Wave for Loss Computations Since the short-range MTOM model must include very short distances and very low antenna heights, propagation is predominantly via the ground wave. The ground-wave signal includes the direct line-of-sight space wave, the ground-reflected wave, and the Norton surface wave that diffracts around the curved Earth or propagates along the surface of a flat Earth. The Earth can be considered flat for all practical purposes in the Short-Range MTOM model. The Norton surface wave will be referred to as simply the surface wave in this report. Propagation of the ground wave depends on the relative geometry of the transmitter and the receiver location and the antenna heights. The radio wave propagates primarily as a surface wave when both the transmitter and the receiver are near the Earth in terms of wavelength, because the direct and ground-reflected waves in the space wave will cancel each other and the surface wave will then be significant. The surface wave is predominantly vertically polarized, since the ground conductivity effectively shorts out most of the horizontal electric field component. What is left of the horizontal field component of the surface wave is attenuated at a rate many times the vertical component of the electric field of the surface wave. When one or both of the antennas are elevated above the ground to a significant height with respect to a wavelength, the space wave predominates. The surface wave propagates along and is guided by the Earths surface. This is similar to the way that an electromagnetic wave is guided along a transmission line. Charges are induced in the Earth by the surface wave. These charges travel with the surface wave and create a current in the Earth. The Earth carrying this current can be represented by a lossy capacitor (a resistance shunted by a capacitive reactance). The characteristics of the Earth as a conductor can therefore be represented by this equivalent parallel RC circuit, where the Earths conductivity can be simulated with a resistor and the Earths dielectric constant by a capacitor. As the surface wave passes over the surface of the Earth, it is attenuated as a result of the energy absorbed by the Earth due to the power loss resulting from the current flowing through the Earths resistance. Energy is taken from the surface wave to supply losses in the ground, and the attenuation of this wave is directly affected by the ground constants of the Earth along which it travels [7]. Figures B-1 through B-30 of Appendix B show a comparison of the computed propagation loss with and without the inclusion of the surface wave over short distances for six different combinations of transmitter and receiver antenna heights, h1 and h2, at frequencies up to 900 MHz. These plots were obtained using the undisturbed-field method and can also be computed using the algebraic expressions for the total electromagnetic field and converting to transmission loss using an equation described later in this report that determines propagation loss as a function of electric-field strength and frequency. Since the losses in Figures B-1 through B-30 represent the ratio of received power to transmitted power, this is a numeric ration less than one, and as a result the loss values in dB are negative. The mutual-coupling method also uses this convention with a received-power to transmitted-power ratio, so the losses are also in negative dB. The undisturbed-field method includes a surface wave and hence makes accurate predictions of propagation loss for the short distances and antennas located close to the ground. The surface

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wave is still present but small at frequencies up to 450 MHz. Above 450 MHz the difference between the curves with and without the surface wave is less than or equal to 1 dB. At 900 MHz the effects of the surface wave are negligible. The surface wave at these higher frequencies in the VHF band actually subtracts from the direct and reflected waves, because it is out of phase with these two waves over most of the path. The net result is a slight increase in propagation loss. A plot at 30 MHz is also shown for comparison where the surface wave is in phase with the direct and reflected waves and they add together, and as a result the addition will reduce the propagation loss. These plots were obtained using the undisturbed-field method, and can be computed from the total electromagnetic field using equations to determine transmission loss. This equation that determines propagation loss as a function of electric field strength and frequency is described later in this report. Notice that the surface wave is more significant for the low antenna heights of one meter for all frequencies, because the surface wave increases with decreasing antenna height. Although the surface wave is generally considered negligible at frequencies at and above 150 MHz for most applications, the surface wave can have a significant effect at these higher frequencies, because of the very short distance requirements that can be as small as one meter for the short-range MTOM model. In addition, the surface wave is also stronger when one or both of the antennas are close to the ground. Therefore, the surface wave should be included for propagation predictions at frequencies at and below 450 MHz. Both the undisturbed-field and mutual-coupling methods to be discussed later in this report include the surface wave in their loss computations.

2.4 The Effects of the Earth on Antenna Patterns at Low Heights Above Earth For low antenna heights, the effects of the close proximity of the Earth to the antenna produce a strong interaction of the antenna patterns with the ground. The antenna pattern performance is vastly different than if the antenna were in free space. If the antenna is within a half wavelength of the ground, the antenna input impedance is also affected, which will affect efficiency and gain. The main beam is generally tilted up in elevation from the horizontal position that it would have had in free space. This causes the antenna to have less low elevation angle coverage. Figures C-1 through C-6 of Appendix C show the elevation antenna patterns for a vertical half-wave dipole at six frequencies for antenna heights of 1, 2, and 3 meters over average ground. Also shown in each figure is the free-space antenna pattern. The antenna patterns over ground are quite different from the free-space antenna patterns and have an increased lobing effect as the frequency increases and the antenna height increases.

2.5 Mutual Coupling Two antennas will always have a mutual coupling present between them, which becomes quite strong when the antenna separation distances are small. In addition, when the antennas are in close proximity to Earth or a large ground plane, there will also be a strong interaction with the antenna images created by the Earth or ground plane. This can have a major influence on the antenna gain, impedance, and radiation patterns. The fields from one antenna will induce

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currents in the other antenna, which will in turn cause radiation from the other antenna and induce currents in the original antenna. A mutual coupling will exist between the two antennas and the images formed by the presence of a ground plane or the Earth. In many cases involving close antenna separations, the mutual coupling between the antennas must be considered when computing propagation loss between the antennas. However, there are scenarios where this effect can be neglected, which will be discussed in the next sections.

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3 METHODS OF COMPUTING PROPAGATION LOSS FOR SHORT DISTANCES AND LOW-ANTENNA HEIGHTS

Several methods were compared in an effort to determine how accurately they can predict propagation loss for low antenna heights and short distances. These methods under consideration included the mutual-coupling method, the undisturbed-field method, and the complex two-ray method. The mutual-coupling method was the most accurate method for prediction of propagation loss. Therefore, the loss prediction method that performs mutual-coupling computations between closely spaced antennas over real ground was used for the initial analysis as a reference and compared to other methods. It was necessary to investigate other methods that could accurately predict propagation loss and compare their results to the mutual-coupling method to see where the simpler methods could replace the mutual-coupling method, because the mutual-coupling method is difficult to implement for a large number of computations of different antenna heights, separation distances, and frequencies. One alternative method for computing propagation loss was the undisturbed-field method, which was much easier to implement than the mutual-coupling method, and could still maintain a high degree of accuracy for propagation loss prediction. The complex two-ray method was compared to both the mutual-coupling and undisturbed-field methods to determine under what conditions it could be used, but it was found to not be accurate for close-in distances and low-antenna heights. A discussion in Section 3.1 of the simple two-ray method and the complex two-ray method will show why these formulas are informative, but inadequate to determine electric fields and propagation loss at close-in distances, but the complex two-ray method can be used at longer distances. Section 3.2 is a discussion of computation methods that will take into account the necessary factors that need to be considered for close-in antenna separations and low-antenna heights. The results of mutual-coupling method computations between two antennas will show where propagation loss can be determined accurately by using this method. These mutual-coupling computations will be compared in Section 3.2 to an alternative computation method that uses the undisturbed electric field and a propagation formula to determine the propagation loss versus distance and frequency. It will be shown that the undisturbed-field method can compute propagation loss with accuracy close to that of the mutual-coupling method by comparison of computations over a wide variety of antenna heights, separation distances, and frequencies. Section 3.3 will compare the undisturbed-field method to the complex two-ray method and the free-space loss method to determine under what conditions of antenna heights, separation distances and frequencies that the simpler methods can be used. Section 3.3 will also discuss the problem with using the free-space term in the power-law propagation formula at distances that are too close for the lower frequencies.

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3.1 Conventional Two-Ray Methods that Only Predict Propagation Loss Approximately A simple two-ray method for predicting radio-wave propagation loss where antenna patterns are not taken into account and the reflection coefficient is set equal to -1.0 does not represent real-world conditions. This method will predict an unrealistic propagation loss versus frequency with very deep nulls and significant lobing structure. The simple two-ray method does not include the effects of antenna patterns. A better two-ray method is one that incorporates the far-field radiation patterns of the antennas and uses the actual reflection coefficient as a function of frequency, incidence angle and ground constants, even though the gains are not valid in the near-field region of the antenna for close-in distance separations. This will be referred to here as the complex two-ray method. Figure 6 compares the simple two-ray method with the complex two-ray method for a frequency of 900 MHz with h1 equal to three meters and h2 equal to one meter with a half-wavelength dipole at the transmitter and receiver antenna locations. The relative dielectric constant of average ground is 15.0 and the conductivity is 0.005 Siemens/meter. Since the losses for both of the two-ray methods are presented as the ratio of received power to transmitted power, the losses are a numeric ratio less than one, and as a result the losses in dB are negative. Notice how much these curves differ, and how the simple two-ray method exaggerates the nulls. Even though the complex two-ray method can make a better prediction of propagation loss than the simple two-ray model, it still does not take into account the significant effects for the short ranges and low antenna heights. More sophisticated methods that do factor in all of the significant effects that are present are discussed in Section 3.2. Comparisons between the complex two-ray method and the more sophisticated methods (based on mutual-coupling and undisturbed-field methods) will show where the complex two-ray method is not adequate at short distances, but can be used as a simpler method at longer distances for LOS scenarios.

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Complex Two-Ray Model h1 = 3 meters, h2 = 1meter (f31900c)Simple Two-Ray Model h1 =3 meters, h2 = 1 meter (f31900s)

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Figure 6. Comparison of simple two-ray model with complex two-ray model at 900 MHz.

3.2 Sophisticated Propagation Loss Prediction Methods that Include All Effects For an even more accurate propagation loss prediction, sophisticated prediction methods would factor in a near-field antenna response when the distances are in the near-field radiation region, and factor in a far-field region antenna radiation pattern when distances are in the far-field region. Two sophisticated methods for propagation loss prediction that factor in these effects were investigated.

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One involves a mutual-coupling computation between two antennas for a prediction of propagation loss. The other involves computation of the undisturbed-electric field, and then determining the loss based on the amplitude of this electric field as a function of distance. The complex two-ray method will be compared to these two sophisticated prediction methods. The undisturbed-field method includes near-field effects, the complex two-ray method, antenna near-field and far-field response, the mutual coup

Propagation Loss Prediction Considerations for Close-In Distances and Low-Antenna Height...

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